At present, Suresh is six times his son's age. 13 years from now, the ratio of ages of Suresh and his son will be 11:4 respectively. Find Suresh's present age ?

Options

A. A)36 yrs
B. B)48 yrs
C. C)30 yrs
D. D)42 yrs

Answer

To find Suresh's present age, we can follow these steps:

### Step 1: Define Variables
Let the present age of Suresh's son be \( x \). Therefore, Suresh's present age will be \( 6x \) since Suresh is six times his son's age.

### Step 2: Set Up Future Age Equation
In 13 years, Suresh's age will be \( 6x + 13 \) and his son's age will be \( x + 13 \). According to the problem, the ratio of their ages at that time will be \( 11:4 \).

### Step 3: Write the Ratio Equation
We can set up the equation based on the ratio:
\[ \frac{6x + 13}{x + 13} = \frac{11}{4} \]

### Step 4: Cross-Multiply
Cross-multiplying gives us:
\[ 4(6x + 13) = 11(x + 13) \]

### Step 5: Expand Both Sides
Expanding both sides:
\[ 24x + 52 = 11x + 143 \]

### Step 6: Rearrange the Equation
Now, rearranging the equation to isolate \( x \):
\[ 24x - 11x = 143 - 52 \]
\[ 13x = 91 \]

### Step 7: Solve for \( x \)
Dividing both sides by 13:
\[ x = \frac{91}{13} = 7 \]

### Step 8: Find Suresh's Present Age
Now, substituting \( x \) back to find Suresh's present age:
\[ \text{Suresh's age} = 6x = 6 \times 7 = 42 \]

### Conclusion
Thus, Suresh's present age is **42 years**.

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